Theorem 3pos

Description: The number 3 is positive. (Contributed by NM, 27-May-1999)

	Ref	Expression
Assertion	3pos	$$⊢0<3$$

Proof

Step	Hyp	Ref	Expression
1		2re	$$⊢2\in ℝ$$
2		1re	$$⊢1\in ℝ$$
3		2pos	$$⊢0<2$$
4		0lt1	$$⊢0<1$$
5	1 2 3 4	addgt0ii	$$⊢0<2+1$$
6		df-3	$$⊢3=2+1$$
7	5 6	breqtrri	$$⊢0<3$$